Question

A rocket is launched vertical from the surface of the earth o radius R with an initial speed v. If atmospheric resistance is neglected , the maximum height attained by the rocket is

• A. $h=\frac{R}{(\frac{2gR}{v^2}-1)}$
• B. $h=\frac{R}{(\frac{2gR}{v^2}+1)}$
• C. $h=\frac{R^2}{(\frac{2gR}{v^2}-1)}$
• D. $h=\frac{R^2}{(\frac{2gR}{v^2}+1)}$

Answer 1

The correct option is A $h=\frac{R}{(\frac{2gR}{v^2}-1)}$

KE of launched rocket = change in PE of rocket on reaching max height

$\frac{1}{2}M{V}^2=Mgh\left[\frac{R}{R+h}\right]$

$\frac{R+h}{R}=\frac{2gR}{V^2}$

$\frac{R}{h}=\frac{2gR}{V^2}-1$

$h=\frac{R}{(\frac{2gR}{V^2}-1)}$